Bubbles in liquids, soft and squeezy objects made of gas and vapour, yet so strong as to destroy any material and so mysterious as at times turning into tiny light bulbs, are the topic of the present report. Bubbles respond to pressure forces and reveal their full potential when periodically driven by sound waves. The basic equations for nonlinear bubble oscillation in sound fields are given, together with a survey of typical solutions. A bubble in a liquid can be considered as a representative example from nonlinear dynamical systems theory with its resonances, multiple attractors with their basins, bifurcations to chaos and not yet fully describable behaviour due to infinite complexity. Three stability conditions are treated for stable trapping of bubbles in standing sound fields: positional, spherical and diffusional stability. Chemical reactions may become important in that respect, when reacting gases fill the bubble, but the chemistry of bubbles is just touched upon and is beyond the scope of the present report. Bubble collapse, the runaway shrinking of a bubble, is presented in its current state of knowledge. Pressures and temperatures that are reached at this occasion are discussed, as well as the light emission in the form of short flashes. Aspherical bubble collapse, as for instance enforced by boundaries nearby, mitigates most of the phenomena encountered in spherical collapse, but introduces a new effect: jet formation, the self-piercing of a bubble with a high velocity liquid jet. Examples of this phenomenon are given from light induced bubbles. Two oscillating bubbles attract or repel each other, depending on their oscillations and their distance. Upon approaching, attraction may change to repulsion and vice versa. When being close, they also shoot self-piercing jets at each other. Systems of bubbles are treated as they appear after shock wave passage through a liquid and with their branched filaments that they attain in standing sound fields. The N-bubble problem is formulated in the spirit of the n-body problem of astrophysics, but with more complicated interaction forces. Simulations are compared with three-dimensional bubble dynamics obtained by stereoscopic high speed digital videography.

Physics of bubble oscillations

Hydrodynamic and hydromagnetic stability

The overflow of cold, dense water from the Nordic seas, across the Greenland-Scotland ridge and into the Atlantic Ocean is the main source for the deep water of the North Atlantic Ocean. This flow also helps drive the inflow of warm, saline surface water into the Nordic seas. The Faroe Bank channel is the deepest path across the ridge, and the deep flow through this channel accounts for about one-third of the total overflow. Previous work has demonstrated that the overflow has become warmer and less saline over time. Here we show, using direct measurements and historical hydrographic data, that the volume flux of the Faroe Bank channel overflow has also decreased. Estimating the volume flux conservatively, we find a decrease by at least 20 per cent relative to 1950. If this reduction in deep flow from the Nordic seas is not compensated by increased flow from other sources, it implies a weakened global thermohaline circulation and reduced inflow of Atlantic water to the Nordic seas.

Decreasing overflow from the Nordic seas into the Atlantic Ocean through the Faroe Bank channel since 1950

A spherical conducting droplet in an alternating electric field is known to undergo shape oscillations. When the droplet is supported by a substrate, the shape is no longer a complete sphere, but shape resonances are still observed. To obtain a completely spherical droplet, some kind of levitation is needed, unless the droplet is in microgravity, and this has previously been provided by gas films or magnetic or other external forces. In this work, we report observations of shape oscillations of a hydrophobic-powder-coated droplet of water. A droplet of water rolled on a hydrophobic powder self-coats such that the water becomes encapsulated as a liquid marble. When the powder is a spherical hydrophobic grain with a contact angle greater than 90 degrees , it adheres to the solid-water interface with more than half of its diameter projecting from the liquid, thus ensuring the encapsulated water does not come into contact with any substrate. These liquid marbles are highly mobile and can be regarded as completely nonwetting droplets possessing contact angles of 180 degrees . In this work, we show that they also provide a new mechanism equivalent to levitating droplets and provide droplets with small contact areas and completely mobile contact lines for studies of shape oscillations. Liquid marbles were created using hydrophobic lycopodium and droplets of water containing potassium chloride and were excited into motion using an electrowetting-on-dielectric configuration with applied frequency swept from 1 to 250 Hz. Both an up-and-down motion and an oscillation involving multiple nodes were observed and recorded using a high-speed camera. The resonant oscillation modes of small liquid marbles were fitted to the theory for vibrations of a free spherical volume of fluid. This work demonstrates the principle that oscillation modes of completely nonwetting droplets can be studied using a simple powder coating approach without the need for an active mechanism for levitation.

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Levitation-Free Vibrated Droplets: Resonant Oscillations of Liquid Marbles

Acoustic levitation uses acoustic radiation forces to counteract gravity and suspend objects in mid-air. Although acoustic levitation was first demonstrated almost a century ago, for a long time, it was limited to objects much smaller than the acoustic wavelength levitating at fixed positions in space. Recent advances in acoustic levitation now allow not only suspending but also rotating and translating objects in three dimensions. Acoustic levitation is also no longer restricted to small objects and can now be employed to levitate objects larger than the acoustic wavelength. This article reviews the progress of acoustic levitation, focusing on the working mechanism of different types of acoustic levitation devices developed to date. We start with a brief review of the theory. Then, we review the acoustic levitation methods to suspend objects at fixed positions, followed by the techniques that allow the manipulation of objects. Finally, we present a brief summary and offer some future perspectives for acoustic levitation.

Review of Progress in Acoustic Levitation

Oscillations of low-viscosity drops were studied in the microgravity environment of a Space shuttle flight. From the damped oscillation data, the inviscid frequency shift, due to nonlinearity, has been extracted using a central-averaging scheme. For the classical case of the oscillations of a free low-viscosity drop, it has been found that the frequency shift agrees well with the predictions of the inviscid nonlinear theory of Tsamopoulos & Brown (1983) for e < 0.3. But for the oscillations of a rotating low-viscosity drop, under acoustic levitation, the frequency shift is smaller, and the percentage of time spent in prolate displacement is significantly less than that for the classical case.

Oscillations of liquid drops : results from USML-1 experiments in Space

Experiments on rotational bifurcation of liquid drops, in which the drops were levitated and spun using acoustic fields in a low-gravity environment, were conducted during the first United States Microgravity Laboratory (USML-1) Space Shuttle flight. The experiments have successfully resolved the discrepancies existing between the previous experimental results and the theoretical predictions. In the case of a spherical drop, for which theory exists, the results agree well with the predictions. In the case of flattened drops, the experiments have extablished a family of curves, with the spherical drop as the limiting case.

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Bifurcation of rotating liquid drops: results from USML-1 experiments in Space

Previous Space-based experiments (Wang et al. 1994a) showed that a rotating liquid drop bifurcates into a two-lobed shape at a lower critical angular velocity, if it is flattened acoustically by the leviating sound field. In this work, we undertake a systematic experimental study of the effect of acoustic flattening on the rotational bifurcation of a liquid drop. We also look into the complementary effect of rotation on the equilibrium of an acoustically drastically flattened drop. Theoretical models are developed for each of the two effects and then woven into a unified picture. The first effect concerns neutral equilibrium, while the second concerns loss of equilibrium, neither of them involving instability. The theories agree well with the experiments.

Equilibrium of liquid drops under the effects of rotation and acoustic flattening: results from USML-2 experiments in Space

The behavior of a liquid drop levitated and drastically flattened byan intense sound field

The dynamics of mixing and satellite drop formation following the coalescence of initially stationary low-viscosity drops of the same liquid has been investigated using immiscible systems. The main parameters of interest are the drop sizes, the drop viscosity and the host viscosity. For drops of equal sizes there is no mixing following coalescence, which is consistent with that first demonstrated on the Skylab. However, for drops of unequal sizes there is considerable mixing with the smaller drop penetrating the larger drop as a vortex. In the extreme case of coalescence of a small drop with the bulk of the same liquid at a flat interface, the measured penetration depth is found to be proportional to the 5/4 th power of the drop diameter and inversely proportional to the square root of drop viscosity. When the drop and host viscosities are comparable, drop penetration is prematurely terminated by the formation of a satellite drop. However, when the drop diameter ratio (large to small) is below a critical number, satellite drop formation is inhibited and coalescence goes to completion. The influence of drop-host viscosity ratio on this critical diameter ratio has been examined.

C. P. Lee

Papers

Oscillations of liquid drops : results from USML-1 experiments in Space

Bifurcation of rotating liquid drops: results from USML-1 experiments in Space

Equilibrium of liquid drops under the effects of rotation and acoustic flattening: results from USML-2 experiments in Space

The behavior of a liquid drop levitated and drastically flattened byan intense sound field

Momentumless coalescence of drops